In the Cobb-Douglas production function $Y = \bar { A } K ^ { a } L ^ { 1 - a }$ , defining y = Y/L as output per person and k = K/L as capital per person, the per person production function is:
A) $y = \bar { A } k ^ { - a }$
B) $y = \bar { A } k ^ { a }$
C) $y = \bar { A } k ^ { 1 - a }$
D) $y = \bar { A } / k ^ { 1 - a }$
E) None of these answers are correct.

Question

Quizplus · Accepted Answer

The per person production function is derived by dividing the original Cobb-Douglas function by L, resulting in $y = \bar { A } k ^ { a }$.

In the Cobb-Douglas Production Function Y=AˉKaL1−aY = \bar { A } K ^ { a } L ^ { 1 - a }Y=AˉKaL1−a

In the Cobb-Douglas Production Function $Y = \bar { A } K ^ { a } L ^ { 1 - a }$